In an AP the sum of first ten terms is -150 and the sum of its next ten terms is -550.Find the AP

In an AP the sum of first ten terms is -150 and the sum of its next te

1.	In an AP the sum of first ten terms is -150 and the sum of its next ten terms is -550.Find the AP
Answer» According to the question,the sum of first 10 terms of an AP is -150 and the sum of its next 10 terms is -550Let a be the first term and d be the common difference of the given AP.Then, we haveS10=-150{tex}\\Rightarrow \\frac { 10 } { 2 } [ 2 a + 9 d ] = - 150{/tex}{tex}\\Rightarrow{/tex}5[2a+9d]=-150{tex}\\Rightarrow{/tex}2a+9d=-30...(i)Clearly, the sum of first 20 terms =-150+(-550)=-700{tex}\\therefore{/tex}S20=-700{tex}\\Rightarrow \\frac { 20 } { 2 } [ 2 a + 19 d ] = - 700{/tex}{tex}\\Rightarrow{/tex}10[2a+19d]=-700{tex}\\Rightarrow{/tex}2a+19d=-70...(iii)Subtracting (i) from (ii), we get10d=-40{tex}\\Rightarrow{/tex}d=-4{tex}\\Rightarrow{/tex}2a=-30-9(-4)=-30+36=6{tex}\\Rightarrow{/tex}a=3Thus, we have\xa0First term=a=3Second term= a+d=3+2(-4)=-1Third term=a+2d=3+2(-4)=3-8=-5Fourth term=a+3d=3+3(-4)=3-12=-9Thus, the given AP is 3,-1,-5,-9,....